quickening speed

Speed

Speed is the rate of motion, or equivalently the rate of change in position, often expressed as distanced traveled per unit of timet.

Speed is a scalarquantity with dimensionsdistance/time; the equivalent vector quantity to speed is known as velocity. Speed is measured in the same physical units of measurement as velocity, but does not contain the element of direction that velocity has. Speed is thus the magnitude component of velocity.

Vehicles often have a speedometer to measure the speed they are going.

Average speed

Speed as a physical property represents primarily instantaneous speed. In real life we often use average speed (denoted |tilde{v}|), which is rate of total distance (or length) and time interval.
For example, if you go 60 miles in 2 hours, your average speed during that time is 60/2 = 30 miles per hour, but your instantaneous speed may have varied.

In mathematical notation:

|tilde{v}| = frac{Delta l}{Delta t}

Instantaneous speed defined as a function of time on interval [t_0, t_1] gives average speed:

|tilde{v}| = frac{int_{t_0}^{t_1} |v|(t) , dt}{Delta t}

while instantaneous speed defined as a function of distance (or length) on interval [l_0, l_1] gives average speed:

|tilde{v}| = frac{Delta l}{int_{l_0}^{l_1} frac{1}

It is often intuitively expected, but incorrect, that going half a distance with speed |v|_{a} and second half with speed |v|_{b}, produces total average speed |tilde{v}| = frac